Here, we have revisited the practical implications of the positivity assumption with focus on the population inferential model,[1]} because epidemiology research is mainly concerned with populations of which only a sample is available.[2]} When the \(n\)  units are the target population, the definitions of deterministic and stochastic positivity coincide. While focus here was centered on positivity related to confounding, other biases and their corresponding exchangeability conditions also rely on positivity assumptions (e.g., missing data,[3]}, [4]} selection bias,[5]}, [6]} measurement error,[7]} and generalizability/transportability[2]}, [9]}). Building on previous work,[10]}, [11]} we laid out how deterministic positivity relates to nonparametric identifiability and stochastic positivity to estimability. Finally, we emphasized how stochastic positivity violations can be ameliorated by additional estimability assumptions, like statistical model specification. While positivity is often overlooked, positivity remains a key assumption that should be examined by epidemiologists.
